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On non-determinism in machines and languages

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Abstract

Non-deterministic computation is not really computation, but the difference with real computation is blurred. We study in detail various levels of non-determinism in computations on non-deterministic Turing machines with polynomial bounds on the resources. Meanwhile, we consider numerous query languages, implicit logic, choice logic, order invariant logic, and restrictions of second-order logic, and establish correspondences between all these formalisms for both deterministic and non-deterministic queries. To the degrees of non-determinism in the computations, correspond levels of non-determinism in the logical definitions. Our main contribution is to characterize various complexity classes between PTIME and PSPACE, by several logical means, thus translating open questions in complexity theory to open questions in logic related to the use of the non-determinism.

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Authors
  1. Stéphane Grumbach
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  2. Zoé Lacroix
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Grumbach, S., Lacroix, Z. On non-determinism in machines and languages. Annals of Mathematics and Artificial Intelligence 19, 169–213 (1997). https://doi.org/10.1023/A:1018955722107

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